Question regarding speeding tickets by way of "pacing"

for the TLDR'ers:
Got a ticket by way of pacing, even though the cop was next to me for about 1/4 mile before turning on his lights/siren and jumping behind to pull me over. How hard is it to fight this method? I usually just pay the ticket and go on my way, but I know I wasn't going as fast as he said since I was set on cruise control.

Long, dramatic version:
Got a ticket today by LSP in Kenner, bruh. Cop merged on at Boutte/310 (heading eastbound into NOLA), I was in the far left lane and he in the far right. Around Loyola I noticed he got up next to me. I checked speedometer, it was still locked in on cruise at 68 from Bonne Carre. About 1/4 mile later, as he is *beside* me, he turns on lights/siren and jumps behind me.

I didn't feel comfortable pulling over there for safety reasons. And it was sprinkling... so there's that thing the rain does to my hair (poodle fro).

Finally got over close to Williams. That must've pissed him off because he yelled at me through his little speaker to get out of the car without anything in my hand. I rolled down my window and said I would prefer to not exit the car as it felt unsafe, but could hand him my info through the window. He proceeded to scream at me through his little microphone to "EXIT THE VEHICLE AND SHOW MY HANDS"...please keep in mind that I am a harmless looking female in a Jackie-O dress, driving a freeking Camry. So, I get out and he says "funny you felt so unsafe but left your driver door half open so someone could clip it"...to which I told him I was concerned for my bodily safety, not the well being of my car door. Then argued with me as to why I was late for my meeting, stating my license said P'ville address yet I said I was coming from BR. Really just acting like an anal sphincter.

He told me I could just go sit in the car to feel safe so he could write my ticket. Once he gifts me with my love letter, I ask how he clocked me since he wasn't radaring. Said he "paced" me even though he was next to me the entire time. I told him I had my cruise set at 68, yet he wrote I was going 71 in a 60. Then I asked how we could really know he was going 70 and me 71, which he said he guessed but could have wrote a higher number....uhh, ok. That's about when I smiled and told him to have a great day.